A systematic fitting scheme for caustic-crossing microlensing events

We outline a method for fitting binary-lens caustic-crossing microlensing events based on the alternative model parametrization proposed and detailed by Cassan. As an illustration of our methodology, we present an analysis of OGLE-2007-BLG-472, a double-peaked Galactic microlensing event with a source crossing the whole caustic structure in less than three days. In order to identify all possible models we conduct an extensive search of the parameter space, followed by a refinement of the parameters with a Markov Chain Monte Carlo algorithm. We find a number of low-  χ²  regions in the parameter space, which lead to several distinct competitive best models. We examine the parameters for each of them, and estimate their physical properties. We find that our fitting strategy locates several minima that are difficult to find with other modelling strategies and is therefore a more appropriate method to fit this type of event.     

On the baseline flux determination of microlensing events detectable with the difference image analysis method

To improve photometric precision by removing the blending effect, a newly developed technique of difference image analysis (DIA) has been adopted by several gravitational microlensing experiment groups. However, the principal problem of the DIA method is that, by its nature, it has difficulties in measuring the baseline flux F ₀ of a source star, causing a degeneracy problem in determining the lensing parameters of an event. Therefore, it is often believed that the DIA method is not as powerful as the classical method based on PSF photometry for determining the Einstein time-scales t _E of events.
In this paper, we demonstrate that the degeneracy problem in microlensing events, detectable from searches using the DIA method, is not as serious as is often thought. This is because a substantial fraction of events will be high amplification events for which the deviations of the amplification curves, constructed with the wrong baseline fluxes from their corresponding best-fit standard amplification curves, will be considerable, even for a small amount of the fractional baseline flux deviation Δ F ₀ F ₀. With a model luminosity function of source stars and under realistic observational conditions, we find that ∼30 per cent of detectable Galactic bulge events are expected to have high amplifications and their baseline fluxes can be determined with uncertainties Δ F ₀ F ₀≤0.5.     

The brown dwarf mass function from pixel microlensing

We argue that gravitational microlensing is a feasible technique for measuring the mass function of brown dwarf stars in distant galaxies. Microlensing surveys of the bulge of M31, and of M87 in the Virgo cluster, may provide enough events to differentiate the behaviour of the mass function of lenses below the hydrogen-burning limit (although we find that M87 is a more favourable target). Such objects may provide a significant supply of baryonic dark matter, an interesting possibility for the study of galactic dynamics. Furthermore, these systems have different metallicities from the solar neighbourhood, which may affect the mass function. These considerations are relevant in the context of star formation studies.     

Variation of spot-induced anomalies in caustic-crossing binary microlensing event light curves

We investigate the pattern of anomalies in the light curves of caustic-crossing binary microlensing events induced by spot(s) on the lensed source star. To this end, we perform simulations of events with various models of spots. From these simulations we find that the spot-induced anomalies take various forms depending on the physical state of spots, which is characterized by the surface brightness contrast, the size, the number, the umbra/penumbra structure, the shape and the orientation with respect to the sweeping caustic. We also examine the feasibility of distinguishing the two possibly degenerate types of anomalies caused by a spot and a transiting planet and find that in many cases the degeneracy can be separated from the characteristic multiple deviation feature in the spot-induced anomaly pattern caused by the multiplicity of spots.     

Predicting the second caustic crossing in binary microlensing events

We fit binary lens models to the data covering the initial part of real microlensing events in an attempt to predict the time of the second caustic crossing. We use approximations during the initial search through the parameter space for light curves that roughly match the observed ones. Exact methods for calculating the lens magnification of an extended source are used when we refine our best initial models. Our calculations show that the reliable prediction of the second crossing can only be made very late, when the light curve has risen appreciably after the minimum between the two caustic crossings. The best observational strategy is therefore to sample as frequently as possible once the light curve starts to rise after the minimum.     

On the astrometric behaviour of binary microlensing events

Despite the suspected binarity for a significant fraction of Galactic lenses, the current photometric surveys detected binary microlensing events only for a small fraction of the total events. The detection efficiency is especially low for non-caustic crossing events, which comprise the majority of the binary lensing events, as a result of the absence of distinctive features in their light curves combined with small deviations from the standard light curve of a single point-mass event. In addition, even if they are detected, it will be difficult to determine the solution of the binary lens parameters owing to the severe degeneracy problem. In this paper, we investigate the properties of binary lensing event expected when they are astrometrically observed by using high-precision interferometers. For this, we construct vector field maps of excess centroid shifts, which represent the deviations of the binary lensing centroid shifts from those of a single lensing event as a function of source position. From the analysis of the maps, we find that the excess centroid shifts are substantial in a considerably large area around caustics. In addition, they have characteristic sizes and directions depending strongly on the source positions with respect to the caustics and the resulting trajectories of the light centroid (astrometric trajectories) have distinctive features, which can be distinguished from the deviations caused by other reasons. We classify the types of the deviations and investigate where they occur. Because of the strong dependence of the centroid shifts on the lens system geometry combined with the distinctive features in the observed astrometric trajectories, astrometric binary lensing observations will provide an important tool that can probe the properties of the Galactic binary lens population.     

The microlensing rate and mass function versus dynamics of the Galactic bar

With the steady increase of the sample size of observed microlenses towards the central regions of the Galaxy, the main source of the uncertainty in the lens mass will shift from the simple Poisson noise to the intrinsic non-uniqueness of our dynamical models of the inner Galaxy, particularly the Galactic bar. We use a set of simple self-consistent bar models to investigate how the microlensing event rate varies as a function of axis ratio, bar angle and velocity distribution. The non-uniqueness of the velocity distribution of the bar model adds a significant uncertainty (by about a factor of 1.5) to any prediction of the lens mass. Kinematic data and self-consistent models are critical to lift the non-uniqueness. We discuss the implications of these results for the interpretation of microlensing observations of the Galactic bulge. In particular we show that Freeman bar models scaled to the mass of the Galactic bulge/bar imply a typical lens mass of around 0.8 M⊙, a factor of 3–5 times larger than the value from other models.     

The non-Gaussian tail of cosmic-shear statistics

Owing to gravitational instability, an initially Gaussian density field develops non-Gaussian features as the Universe evolves. The most prominent non-Gaussian features are massive haloes, visible as clusters of galaxies. The distortion of high-redshift galaxy images because of the tidal gravitational field of the large-scale matter distribution, called cosmic shear, can be used to investigate the statistical properties of the large‐scale structure (LSS) . In particular, non-Gaussian properties of the LSS will lead to a non-Gaussian distribution of cosmic-shear statistic. The aperture mass ( M _ap) statistics, recently introduced as a measure for cosmic shear, is particularly well suited for measuring these non-Gaussian properties. In this paper we calculate the highly non-Gaussian tail of the aperture mass probability distribution, assuming Press–Schechter theory for the halo abundance and the 'universal' density profile of haloes as obtained from numerical simulations. We find that for values of M _ap much larger than its dispersion, this probability distribution is closely approximated by an exponential, rather than a Gaussian. We determine the amplitude and shape of this exponential for various cosmological models and aperture sizes, and show that wide-field imaging surveys can be used to distinguish between some of the currently most popular cosmogonies. Our study here is complementary to earlier cosmic-shear investigations, which focused more on two- and three-point statistical properties.     

Effects of cluster galaxies on arc statistics

We present the results of a set of numerical simulations evaluating the effect of cluster galaxies on arc statistics.
We perform a first set of gravitational lensing simulations using three independent projections for each of nine different galaxy clusters obtained from N -body simulations. The simulated clusters consist of dark matter only. We add a population of galaxies to each cluster, mimicking the observed luminosity function and the spatial galaxy distribution, and repeat the lensing simulations including the effects of cluster galaxies, which themselves act as individual lenses. Each galaxy is represented by a spherical Navarro, Frenk & White density profile.
We consider the statistical distributions of the properties of the gravitational arcs produced by our clusters with and without galaxies. We find that the cluster galaxies do not introduce perturbations strong enough to significantly change the number of arcs and the distributions of lengths, widths, curvature radii and length-to-width ratios of long arcs. We find some changes to the distribution of short-arc properties in the presence of cluster galaxies. The differences appear in the distribution of curvature radii for arc lengths smaller than 12 arcsec, while the distributions of lengths, widths and length-to-width ratios are significantly changed only for arcs shorter than 4 arcsec.     

Another channel to detect close-in binary companions via gravitational microlensing

Gaudi & Gould showed that close companions of remote binary systems can be efficiently detected by using gravitational microlensing via the deviations in the lensing light curves induced by the existence of the lens companions. In this paper, we introduce another channel to detect faint close-in binary companions by using microlensing. This method utilizes a caustic-crossing binary lens event with a source also composed of binary stars, where the companion is a faint star. Detection of the companion is possible because the flux of the companion can be highly amplified when it crosses the lens caustic. The detection is facilitated since the companion is more amplified than the primary because it, in general, has a smaller size than the primary, and thus experiences less finite source effect. The method is an extension of the previous one suggested to detect close-in giant planets by Graff & Gaudi and Lewis & Ibata and further developed by Ashton & Lewis. From the simulations of realistic Galactic bulge events, we find that companions of K-type main-sequence or brighter stars can be efficiently detected from the current type of microlensing follow-up observations by using the proposed method. We also find that compared with the method of detecting lens companions for which the efficiency drops significantly for binaries with separations ≲0.2 of the angular Einstein ring radius, θ _E, the proposed method has an important advantage of being able to detect companions with substantially smaller separations down to ∼     .     

Astrometric microlensing: a channel to detect multiple lens systems

If a source star is gravitationally microlensed by a multiple lens system, the resulting light curve can have significant deviations from the standard form of a single lens event. The chance of producing significant deviations becomes important when the separations between the component lenses are equivalent to the combined angular Einstein ring radius of the system. For multiple lens systems composed of more than two lenses, however, this condition is difficult to meet because the orbits of such systems are unstable. Even if events are caused by a multiple lens system with stable orbits where a pair of lenses are closely located and the other component (a third body) has a wide separation from the pair, identifying the lens multiplicity photometrically will be difficult because the event will be identified by either a binary lens event caused by the close pair of lenses or a single lens event caused by the third body. In this paper, we show that if a seemingly binary lens event is followed up astrometrically using future high-precision interferometers, the existence of an additional third body can be identified via a repeating event. We show that the signatures of third bodies can be unambiguously identified from the characteristic distortions they make in the centroid shift trajectories. We also show that owing to the long-range astrometric effect of third bodies, the detection efficiency will be considerable even for third bodies with large separations from their close lens pairs.     

The observed concentration–mass relation for galaxy clusters

The properties of clusters of galaxies offer key insights into the assembly process of structure in the universe. Numerical simulations of cosmic structure formation in a hierarchical, dark matter dominated universe suggest that galaxy cluster concentrations, which are a measure of a halo's central density, decrease gradually with virial mass. However, cluster observations have yet to confirm this correlation. The slopes of the run of measured concentrations with virial mass are often either steeper or flatter than that predicted by simulations. In this work, we present the most complete sample of observed cluster concentrations and masses yet assembled, including new measurements for 10 strong-lensing clusters, thereby more than doubling the existing number of strong-lensing concentration estimates. We fit a power law to the observed concentrations as a function of virial mass, and find that the slope is consistent with the slopes found in simulations, though our normalization factor is higher. Observed lensing concentrations appear to be systematically larger than X-ray concentrations, a more pronounced effect than that found in simulations. We also find that at a fixed mass, the bulk of observed cluster concentrations are distributed lognormally, with the exception of a few anomalously high concentration clusters. We examine the physical processes likely responsible for the discrepancy between lensing and X-ray concentrations, and for the anomalously high concentrations in particular. The forthcoming Millennium simulation results will offer the most comprehensive comparison set to our findings of an observed concentration–mass power law relation.     

Repeating microlensing events in the OGLE data

Microlensing events are usually selected among single-peaked non-repeating light curves in order to avoid confusion with variable stars. However, a microlensing event may exhibit a second microlensing brightening episode when the source or/and the lens is a binary system. A careful analysis of these repeating events provides an independent way to study the statistics of wide binary stars and to detect extrasolar planets. Previous theoretical studies predicted that 0.5–2 per cent of events should repeat due to wide binary lenses. We present a systematic search for such events in about 4000 light curves of microlensing candidates detected by the Optical Gravitational Lensing Experiment (OGLE) towards the Galactic bulge from 1992 to 2007. The search reveals a total of 19 repeating candidates, with six clearly due to a wide binary lens. As a by-product, we find that 64 events (∼2 per cent of the total OGLE-III sample) have been misclassified as microlensing; these misclassified events are mostly nova or other types of eruptive stars. The number and importance of repeating events will increase considerably when the next-generation wide-field microlensing experiments become fully operational in the future.